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Chapter 1: Problem 16

Determine whether the equation represents \(y\) as a function of \(x .\) $$y=\sqrt{x+5}$$

Short Answer

Expert verified
The equation \(y = \sqrt{x+5}\) does represent \(y\) as a function of \(x\).

Step by step solution

01

Setting the equation

The given equation is \(y = \sqrt{x+5}\).
02

Understanding the square root function

The square root function, \(f(x) = \sqrt{x}\), outputs one value for every \(x\) in its domain. Here, \(x\) must be greater or equal to \(-5\) to keep the expression under the square root non-negative. This is because the square root of a negative number is not defined in the real number system.
03

Verifying that y is a function of x

For every value of \(x\) (greater than or equal to \(-5\)), the equation \(y = \sqrt{x+5}\) yields exactly one value of \(y\), which follows the definition of a function. Therefore, \(y\) is indeed a function of \(x\) in this equation.

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